The task is to analyze and solve the problem presented in the image. Let me transcribe the problem for clarity:

Transcription of the problem:

Первая труба пропускает на 5 литров воды в минуту меньше, чем вторая труба. Сколько литров воды в минуту пропускает первая труба, если резервуар объемом 200 литров она заполняет на 2 минуты дольше, чем вторая труба?

Translation (for solving):

The first pipe passes 5 liters of water per minute less than the second pipe. How many liters of water per minute does the first pipe pass if it fills a 200-liter tank 2 minutes longer than the second pipe?

Solution:

Let:

• $x$: The rate of the second pipe (liters per minute).
• $x - 5$: The rate of the first pipe (liters per minute).

Time taken to fill the tank:

• For the first pipe: $\frac{200}{x - 5}$ minutes.
• For the second pipe: $\frac{200}{x}$ minutes.

The difference in time is given as 2 minutes: $\frac{200}{x - 5} = \frac{200}{x} + 2$

Step 1: Eliminate fractions by multiplying through by $x(x - 5)$:

$200x = 200(x - 5) + 2x(x - 5)$

Step 2: Expand and simplify:

$200x = 200x - 1000 + 2x^2 - 10x$ $0 = 2x^2 - 10x - 1000$

Step 3: Simplify the quadratic equation:

$x^2 - 5x - 500 = 0$

Step 4: Solve using the quadratic formula:

$x = \frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-500)}}{2(1)}$ $x = \frac{5 \pm \sqrt{25 + 2000}}{2}$ $x = \frac{5 \pm \sqrt{2025}}{2}$ $x = \frac{5 \pm 45}{2}$

Step 5: Find the two solutions:

$x = \frac{50}{2} = 25 \quad \text{or} \quad x = \frac{-40}{2} = -20$

Since the flow rate cannot be negative: $x = 25 \, \text{liters per minute (rate of the second pipe)}.$

Step 6: Find the rate of the first pipe:

$x - 5 = 25 - 5 = 20 \, \text{liters per minute}.$

Final Answer:

The first pipe passes 20 liters of water per minute.

Would you like additional details or a breakdown of a specific step?
Here are 5 related questions you might find interesting:

1. How would the result change if the difference in time were 3 minutes instead of 2?
2. What happens if the tank volume changes to 300 liters?
3. Can this problem be solved graphically? If so, how?
4. How do different flow rates affect the efficiency of such systems?
5. Can similar equations be applied to multi-pipe systems?

Tip: Always check the feasibility of solutions by substituting back into the original problem!